> Again, one really simple fix to eliminate these ERRORS

Well, what you are looking for is Maple, Mathematica or Octave, some
kind of symbolic mathematics software.
They all have worked very hard to make all those kind of things
consistent in a mathematical point of view. But even there you can
still quite easily find "mathematical bugs" that is results that are
not in the simplest form expected even by my least gifted students.

Cheers,

-- 
JJ Fleck
PCSI1 Lyc˝Ă Kl˝├er